The viscous LSD units I have seen (in FWD and AWD gearbox) are sealed, so changing the diff oil would not make any difference.
The myth goes like this, if your diff is noisy you can put a banana skin in there and it will quiten it up for a short time, long enough to sell the car.
I tried this, it sort of works. Nothing to do with LSD. It would make the oil a little thicker for a short time. You would get a similar result if you used diff oil for a Mack truck.